We study existence, bifurcation and stability of two-dimensional optical solitons in the
framework of fractional nonlinear Schrödinger equation, characterized by its Lévy index, with …

We address the existence and stability of vortex-soliton (VS) solutions of the fractional
nonlinear Schrödinger equation (NLSE) with competing cubic-quintic nonlinearities and the …

Abstract We introduce axisymmetric Airy-Gaussian vortex beams in a model of an optical
system based on the (2+ 1)-dimensional fractional Schrödinger equation (FSE) …

We construct a family of bright optical solitons composed of fundamental-frequency (FF) and
second-harmonic (SH) components in the one-dimensional (planar) waveguide with the …

Interest in physical systems with fractional derivatives has exploded in the 21st century.
Similarly, interest in the localized excitations of nonlinear dynamical systems continues to …

We report symmetric and antisymmetric solitons in the fractional nonlinear Schrödinger
equation with the defocused saturable nonlinearity and the PT-symmetric potential. Both …

We study symmetry breaking of solitons in the framework of a nonlinear fractional
Schrödinger equation (NLFSE), characterized by its Lévy index, with cubic nonlinearity and …

We elaborate a fractional discrete nonlinear Schrödinger (FDNLS) equation based on an
appropriately modified definition of the Riesz fractional derivative, which is characterized by …

We demonstrate that the fractional cubic-quintic nonlinear Schrödinger equation,
characterized by its Lévy index, maintains ring-shaped soliton clusters (“necklaces") carrying …

We discover a series of ring and cluster solitons in the (1+ 2)-dimensional nonlocal
nonlinear fractional Schrödinger equation by iteration algorithm, and verify their robustness …